Category: Knots

The gripfid is an invention of knotting expert Stuart Grainger.^[1] It is a small knotter’s fid with an added “grip”, a hollow shaft that ends near the point with a vee that acts as a jamming cleat.

For ply-split braiding the point separates plies, and another cord is tucked into the hollow shaft of the gripfid and pulled back through the split cord. Although a latchhook may be used instead of a gripfid, the latter is much preferred.^{[2][3][4][5][6]}

Water bowline
Category	Loop
Related	double bowline
Releasing	Non-jamming
Typical use	Wet conditions
ABoK	#1012

The water bowline is a type of knot designed for use in wet conditions where other knots may slip or jam.

Although similar in finished appearance to the double bowline, the water bowline is formed with a clove hitch as the loop in the standing part of the rope. This is similar to the double bowline, which puts the running end through a round turn. The additional friction from the clove hitch increases the security of this knot.

• 
  1. Make a half hitch
• 
  2. Complete the clove hitch

• 
  3. Through the clove hitch
• 
  4. Around standing end
• 
  5. Back through hitches

The Water Bowline can be tied very quickly by throwing two half hitches over the working end and then running the working end around the standing line and back through both half hitches. This is illustrated in the three pictures below.

• 
  Throw the first hitch
• 
  Throw the second hitch
• 
  Complete the knot

• List of knots

• Little Campfires (2020-08-01). “How to Tie a Bowline Knot (Plus Variations): Water Bowline”. YouTube.
• TheTautLine (2023-09-11). “Complete Guide to the Bowline Knot and its Most Important Variants: Water Bowline”. YouTube.
• Water bowline knot

Grief knot
Names	Grief knot, What knot, Whatnot, Grass bend, Reeving-line bend
Category	Trick
Category 2	Bend
Related	Reef knot, Thief knot, Granny knot
Releasing	Non-jamming
Typical use	Used for jokes and tricks. It unrolls itself under a light load.
Caveat	Highly insecure
ABoK	#1208, #1406, #1407, #1459, #1490, #2579, #259

A grief knot (also what knot) is a knot which combines the features of a granny knot and a thief knot, producing a result which is not generally useful for working purposes. The word grief does not carry its usual meaning but is a portmanteau of granny and thief.

The grief knot resembles the granny knot, but tied so that the working ends come out diagonally from each other, whereas a granny knot’s ends both come out on the same side. It unravels rather elegantly: as tension is applied, the ropes rotate like little cogs, each one twisting to feed the rope through the knot.^[1]

The whatnot. This is the same knot formation as the granny knot, but the ends are diagonally opposite each other. It is hardly a practical knot. But with the ends seized it is called the reeving line bend, and it also serves as an interesting trick.

To tie the grief knot, tie a single “overhand knot” (nb: this isn’t the same as a single-strand “overhand knot” often used as a stopper or as a component of other knots, such as the fisherman’s knot or ring water knot), as if starting a reef knot. Then thrust the two free ends together down through the center of the just-tied overhand knot.^[3] Twist the free ends to form half hitches to lock, twist the other way for the granny knot-like configuration that rolls apart when the standing parts are pulled. In short, if the standing parts (the “main lines” which bear force into the knot) nip/cross their own ends, the knot will lock; otherwise, it will probably slip.

The starkly differing behavior of the knot, depending on how it is arranged, has been exploited as the basis of a parlor trick.^[1] When pulling on the standing ends the knot starts slipping and the working ends become crossed. By twisting the working ends so that they uncross and then recross in reverse, the knot’s structure is changed so that it will no longer slip. The twisting motion has been paralleled to the turning of a key, “locking” and “unlocking” the knot.

Because the grief knot is known to slip apart “with astonishing ease”,^[3] it is considered one of the most insecure of knots.^[4]

However, in its locked opposing half-hitch arrangement, the grief knot has been used as a practical bend for tying together flat materials, such as straps, belts, blades of grass, and similar materials. This is because the flat shape helps to prevent the knot from accidentally “unlocking”. When used in this manner, the knot is known as a grass bend.^[5]

• 
  Reef (square) knot
• 
  Thief knot
• 
  Granny knot
• 
  Grief knot
• 
  Surgeon’s knot

• List of binding knots
• List of knots

• The Reef Knot Family Archived 2013-12-03 at the Wayback Machine

Warazan (藁算) was a system of record-keeping using knotted straw at the time of the Ryūkyū Kingdom.^[3][4] In the Southern Ryukyuan languages of the Sakishima Islands it was known as barazan and on Okinawa Island as warazani or warazai.^[5] Formerly used in particular in relation to the “head tax”, it is still to be found in connection with the annual Itoman Giant Tug-of-War (糸満大綱引), to record the amount of miki or sacred sake dedicated.^[1]

• Kaidā glyphs
• Naha Tug-of-war
• Quipu

The Grantchester knot is a self-releasing, asymmetric way of tying a necktie.
Using the notation presented in The 85 Ways to Tie a Tie, it is a Lo Ri Lo Ri Co Li, finishing with Ro Li Co T.

• Grantchester knot instructions
• 
  Lo beginning
• 
  Ri
• 
  Lo
• 
  Ri
• 
  Co, Li
• 
  Ro Li Co T end.

• Demonstration of how to tie a Grantchester Knot on YouTube
• Open Directory Project Reference: Knots: Neckties

Wall and crown knot
Names	Wall and crown knot, Manrope knot
Category	Decorative
Related	Turk’s head knot, Underwriter’s knot
ABoK	#672, #847
Instructions

A wall and crown knot is a decorative kind of rope button. The original use of the knot was to put at the end of the ropes on either side of a gangway leading onto a ship as stoppers.

The knot consists of a wall knot and a crown knot with doubled strands.^[1] The strands of the wall knot go over, under twice, and over, while the strands of the crown knot go under, over twice, and under. In the wall and crown knot they are tied in opposite directions.

This knot is often confused with a Turk’s head knot, as both knots have a basket weave pattern.

A Manrope knot (double wall and crown, #847) is the same knot as wall and crown knot, but with little changes – crown strands doubled or tripled. In Verrill’s book it is made from three-strand and crown strands doubled, in Ashley’s book it is made from four-strand and crown strands tripled.

Crown knot
Names	Crown knot, single crown,[2] three strand crown[3]
Category	Decorative
ABoK	670

A crown knot^[3] is the simplest of the fancy knots.^[2] It is created from three strands.

670. “Crowning” is mentioned by Steel in 1794. The Vocabulary of Sea Phrases of 1799 gives both the crown and the double crown…To tie a three-strand crown: Hold the apparatus as in the right upper diagram, and tie the knot in a counterclockwise direction. Take one strand, and cross it over the next strand ahead. Take the second strand, cross it over the end of the first-moved strand and across the standing part of the next strand ahead. Take the third strand, and cross it over the end of the strand last moved, then tuck the end through the bight of the next strand ahead (which, in the Three-Strand Knot, is the first strand that was moved). Draw the knot up, and it will appear as in the last two diagrams.

• 
  Crown (top view)
• 
  Crown tucked
• 
  Double crown

Wall knot
Category	Decorative
ABoK	671

A wall knot^[2][3] is essentially a crown knot, but reversed.^[2][4]

671. The wall knot is the exact reverse of the crown knot. If either of these knots is turned upside down it becomes the other knot. But as the stem of a knot leads from the bottom, the knots ordinarily are different.

John Smith mentions the “wall knot” in 1627, Manwayring the “wale knot” in 1644, Blanckley the “whale knott” in 1750, and Falconer the “Walnut” in 1769. Even in Falconer’s day standardized spelling and pronunciation had hardly been thought of…To tie a three-strand wall knot: Take one strand and bring it counterclockwise under the next strand. Take the next strand, and pass it under the end of the first-moved strand and under the standing part of the next. Take the third strand under the second end and up through the bight of the first-moved strand.

• 
  Double wall
• 
  Wall crowned
  (unfinished “wall and crown knot”)

• List of knots
• Eye splice
• Underwriter’s knot — two-strand wall knot

• 
  Crown knot
• 
  Wall knot
• 
  Wall and crown knot
• 
  Shroud knot
• 
  French shroud
• 
  Matthew Walker knot
• 
  Rose knot
• 
  Tying of Rose knot

• “Manrope Knot“, Marinews.com. Accessed: March 2013.

Granny knot
Names	Granny knot, false knot, lubber’s knot, calf knot, booby knot
Category	Binding
Origin	Ancient
Related	Reef knot, thief knot, grief knot
Releasing	Often jams
Caveat	Should not be used as a bend. Inferior to reef knot for binding purposes, it can release suddenly and unpredictably.
ABoK	#3, #80, #186, #464, #1206, #1405, #2553

The granny knot is a binding knot, used to secure a rope or line around an object. It is considered inferior to the reef knot (square knot), which it superficially resembles. Neither of these knots should be used as a bend knot for attaching two ropes together.

The granny knot is also called the false, lubber’s, calf, and booby knot. Patterson’s Nautical Encyclopedia calls it “old granny knot” and Sir Edwin Arnold calls it the “common or garden knot.” The name granny is given in Vocabulary of Sea Phrases (Anonymous, 1799) and Roding pictures the knot in 1795.

The granny consists of two identical half knots, one tied on top of the other. It has but one practical purpose that I know of and that is to serve as a surgeon’s knot. Formerly it was employed for tying up parcels in five-and-ten-cent stores, but the practice was given up and paper bags substituted as they were found to be simpler.

Called the “granny’s knot” with references going back to at least 1849, the knot was so-called because it is “the natural knot tied by women or landsmen”.^[2][3]

When attempting to tie a reef knot (square knot), it is easy to produce a granny knot accidentally. This is dangerous because the granny knot can slip when heavily loaded. A tightened granny knot can also jam and is often more difficult to untie than the reef knot. It is better to tie a reef knot in nearly all circumstances. One way to distinguish them is that in the reef knot each loop passes completely over, or completely under (not through) the neck of the other.

The reef knot is commonly taught as left over right, tuck under then right over left, tuck under. The granny knot is the first step repeated twice, left over right, tuck under. This is a very common mistake made by people learning to tie a reef knot.

In heraldry, the granny knot is known as the Bourchier knot, due to being a heraldic badge of the Bourchier family.^[4]

• 
  Reef (square) knot
• 
  Thief knot
• 
  Granny knot
• 
  Grief knot
• 
  Surgeon’s knot

• List of binding knots
• List of knots

• “The Reef Knot Family Archived 2013-12-03 at the Wayback Machine”, NotableKnotIndex.webs.com.

Wake knot
The Wake badge.
Information
Family	Wake family
Region	Lincolnshire

The Wake knot or Ormond knot is an English heraldic knot used historically as an heraldic badge by the Wake family, lords of the manor of Bourne in Lincolnshire and also by the Butler family, Earls of Ormond.

It takes the form of a Carrick bend knot connecting two ropes but the Wake knot shows the knot joining a rope and a strap.

It is depicted in the coat of arms of Bourne Town Council^[2] and Bourne Academy, Lincolnshire, where the Wakes were lords of the manor.

The crest of the arms of the Isle of Ely County Council was a human hand grasping a trident around which an eel was entwined; on the wrist of the hand was a Wake knot, representing Hereward the Wake.^[3]

The crest of No. 2 Squadron RAF includes a Wake knot. Its motto is Hereward.

In mathematics, the Gordon–Luecke theorem on knot complements states that if the complements of two tame knots are homeomorphic, then the knots are equivalent. In particular, any homeomorphism between knot complements must take a meridian to a meridian.

The theorem is usually stated as “knots are determined by their complements”; however this is slightly ambiguous as it considers two knots to be equivalent if there is a self-homeomorphism taking one knot to the other. Thus mirror images are neglected. Often two knots are considered equivalent if they are isotopic. The correct version in this case is that if two knots have complements which are orientation-preserving homeomorphic, then they are isotopic.

These results follow from the following (also called the Gordon–Luecke theorem): no nontrivial Dehn surgery on a nontrivial knot in the 3-sphere can yield the 3-sphere.

The theorem was proved by Cameron Gordon and John Luecke. Essential ingredients of the proof are their joint work with Marc Culler and Peter Shalen on the cyclic surgery theorem, combinatorial techniques in the style of Litherland, thin position, and Scharlemann cycles.

For link complements, it is not in fact true that links are determined by their complements. For example, JHC Whitehead proved that there are infinitely many links whose complements are all homeomorphic to the complement of the Whitehead link. His construction is to twist along a disc spanning an unknotted component (as is the case for either component of the Whitehead link). Another method is to twist along an annulus spanning two components. Gordon proved that for the class of links where these two constructions are not possible there are finitely many links in this class with a given complement.

• Cameron Gordon and John Luecke, Knots are determined by their complements. J. Amer. Math. Soc. 2 (1989), no. 2, 371–415.
• Cameron Gordon, Links and their complements. Topology and geometry: commemorating SISTAG, 71–82, Contemp. Math., 314, Amer. Math. Soc., Providence, RI, 2002.

The vortex theory of the atom was a 19th-century attempt by William Thomson (later Lord Kelvin) to explain why the atoms recently discovered by chemists came in only relatively few varieties but in very great numbers of each kind. Based on the idea of stable, knotted vortices in the ether or aether, it contributed an important mathematical legacy.

The vortex theory of the atom was based on the observation that a stable vortex can be created in a fluid by making it into a ring with no ends. Such vortices could be sustained in the luminiferous aether, a hypothetical fluid thought at the time to pervade all of space. In the vortex theory of the atom, a chemical atom is modelled by such a vortex in the aether.

Knots can be tied in the core of such a vortex, leading to the hypothesis that each chemical element corresponds to a different kind of knot. The simple toroidal vortex, represented by the circular “unknot” 0₁, was thought to represent hydrogen. Many elements had yet to be discovered, so the next knot, the trefoil knot 3₁, was thought to represent carbon.

Between 1870 and 1890 the vortex atom theory, which hypothesised that an atom was a vortex in the aether, was popular among British physicists and mathematicians. William Thomson, who became better known as Lord Kelvin, first conjectured that atoms might be vortices in the aether that pervades space. About 60 scientific papers were subsequently written on it by approximately 25 scientists.

Peter Tait

Thomson’s colleague Peter Guthrie Tait was attracted by the vortex atom theory and undertook a pioneering study of knots, producing a systematic classification of those with up to 10 crossings, in the hope of thus systematizing the various elements.

• Loop quantum gravity
• Magnetic skyrmion, a vortex-like magnetic quasiparticle
• Quantum vortex, a quantised flux circulation
• Toroidal ring model of elementary particles